Time series are data observed over time (either in continuous time or at discrete time periods).

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Forecasting in R using forecast package

I'm trying to forecast hourly data for 30 days for a process. I have used the following code: ...
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25 views

Characterizing trend of time series in R

I have a fairly basic statistics application question. Lets say I have a set of four fold-change values, representing the abundance of a factor as it passes through four consecutive time points: ...
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35 views

Cluster analysis on time series samples

In the follow-up to this Ways to understand 2-dimensional time-series data I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and ...
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57 views

Whitening Transformation using a Hadamard product Variance Matrix

I want to whiten a vector $X$ by transforming the variance-covariance matrix so the variance-covariance matrix of the transformed series will be the identity matrix $I$. $X$ is a time-series column ...
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73 views

Difference between series with drift and series with trend

A series with drift can be modeled as $y_t = c + \phi y_{t-1} + \epsilon_t$ where $c$ is the drift(constant), and $\phi=1$ A series with trend can be modeled as $y_t = c + \delta t + \phi y_{t-1} + ...
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13 views

Difficult to understand the meaning of ergodicity and ensemble averaging

Chaotic Signal Processing, pg147--148 describes how a signal (output of laser) operating in chaotic regime is ergodic. Literature says that a stationary signal is ergodic, if its ensemble average = ...
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15 views

How to conduct the two sample test with extra data to eliminate between-subjects variability

I am stuck with the correlated and independent data combined in one study. Here's my dilemma: Say X is a drug(explanatory variable) and Y is a gene expression(response variable). Normally, you ...
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21 views

How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? [duplicate]

Suppose we have a time series $X_t$ s.t. $X_t \sim^{iid} (0,1)$. How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? Or, I guess, if ...
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77 views

Ways to understand 2-dimensional time-series data

I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and saw its variation over time, the fluctuation occurs at few places only. I'm ...
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2answers
43 views

Imputing missing observation in multivariate time series

Suppose I have a dataframe consisting of six time series. In this dataframe, some observations are missing, meaning at some timepoints all time series contain a NA-value. In R, one possible imputation ...
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7 views

Repeated measures with multiple time points for the predictor and dependent variable: Does Xt-1 predict Yt better than Yt-1 predict Xt?

I have a question on what type of analysis I should be looking into to analyze some data I have: Suppose you have 2 runners X and Y, and they take turns sprinting 100 meters, with runner X going ...
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9 views

How many quarters of observations are suggested before and after an event to determine the events significance in a time series analysis?

I'm reviewing a multiple regression time series analysis, and I'm concerned about the (possibly insufficient) sample size. The goal of the analysis is to determine whether an event during the time ...
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1answer
42 views

Repeated measures ANOVA design/structural issue

As part of my PhD work, I've conducted an inoculation experiment concerned with marine phytoplankton community productivity (dependant variable, as 'no. of cells') vs nutrient availability. I have two ...
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1answer
32 views

Markov Chain State Transition Probability in R

I have a dataset which shows the states (3 states) across 11 time points for each participant. I wanted to estimate the Markov Chain state transition probability matrices for time points 2-11 using R. ...
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2answers
51 views

Time Series on Oil Filter Pressure

I am not really strong with time series but I have a project I am working on.. I have a problem where I am trying to model a time series of the difference in pressure before and after oil has passed ...
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1answer
51 views

$R^2$ correspondence for nonlinear time series

Is there a statistical measure for nonlinear time series data that is comparable to $R^2$ value in linear regression (giving an idea of how well the fit is)? The data is not monotonic, so I cannot ...
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1answer
53 views

Creating a composite rank of restaurants with some missing data

I have monthly sales data of 500 restaurants for one year. For the same restaurants, I also have customer defection or dissatisfaction rates. I want to create a composite score that can rank ...
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80 views

Machine-Learning algorithms for Forecasting

For work, I'm working on an app where you essentially forecast the failure rate of the overall machine through different factors such as the historical failure rates for the components used to build ...
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1answer
50 views

Need clarity on alpha, beta, gamma optimization in Triple Exponential Smoothing Forecast

I asked a variation of this question, but I want to be more direct. Take the exact same Triple Exponential Smoothing Model (Holt-Winters with a moving level, trend, and seasonal component)--- Would ...
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25 views

How to estimate the point of divergence between two continuous time survival curves?

In this experiment we collect $N$ samples and each sample yields a pair of survival curves. The two survival curves are hypothesized to be identical up until time $t$ and diverge thereafter. What ...
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1answer
46 views

structural breaks in time series using matlab

in a plot of my time series there is clearly visible that there is structural break, but I have to find the exact date. I want test this with the chow test. Although I understand how to perform this ...
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41 views

Time series, x-y coordinates, regression, R [closed]

I have data in the form of these columns: date, x coordinate, y coordinate, value A, value B, value C, value D, etc. (I don't see the possibility to copy an ...
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1answer
25 views

Correlation definition between two set

How can I define correlation between two set x and y: {$(x_1,y_1),(x_2,y_2),(x_3,y_3),...(x_n,y_n)$} Is this definition correct: ...
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40 views

R GMM - Error in solve.default(x$v, gb) : system is computationally singular: reciprocal condition number

I'm having the following problem estimating something in GMM in R. I have created a "Hello World" below. In principle, I would not need GMM to estimate the parameters, but I want to use it to obtain ...
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1answer
50 views

F test to test equality of variance

I have a single time series which will be divided on the date of the policy change before and after. I want to compare the variances between the two time sections and I am told to do an F test of ...
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2answers
50 views

Forecasting: Different Model for 1 month, 2 month, 6 month forecasts?

I'm still trying to expand my statistics and forecasting technique knowledge. Right now I'm forecasting seasonal contact patterns, so the simplest model I can understand with seasonality is a ...
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22 views

What would be an ideal measure for the synchrony of laughter?

I am exploring the relationship between the quality of connection two people share and the tendency for their laughter to synchronize. In order to do this, I need some way to quantify the degree of ...
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33 views

Transforming time series of different time horizon to stationary

I have a list of monthly time series data with different time periods and different order of integration. I want to transform them all to stationary and a same time period. I noticed that the order ...
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1answer
56 views

Multicollinearity with Interaction (high VIF)

When I check the VIF of my independent variables with the dependent variable, it looks normal and less than 5 but when I add the interaction variables, the VIF increase to 48 for some variables. I ...
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36 views

understand forecasts in linear state space models

The Kalman Filter provides the one-step-ahead forecasts within the recursions. We start estimating the (unkown) variance of the parameters for instance through MCMC ...
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50 views

First order autocorrelation of a certain AR process

How could I compute the first order autocorrelation of the process $x_t = \delta + \phi x_{t-1} + \eta_t$? Could anyone give me some pointers? I tried this: $E(\delta + \phi x_{t-1} + \eta_t - ...
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18 views

Hp testing on cointegrating vectors of an identified VECM

I have estimated a VECM model, then I have used linear restrictions to identify and over-identify my model. Now I have the following output. How can I test the significance of the coefficients in the ...
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1answer
53 views

what is K in fourier function of R

I am using fourier() function of R which has arguments x,h,K. Can any body please explain me what is 'K' in this function and what is the use of it. Thanks in ...
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61 views

Prove expression for variance AR(1)

For the AR(1) process $x_t = \delta + \phi x_{t-1} + \eta_t$, I am trying to prove that the variance is: $\sigma_x^2 = \sigma_\eta^2/(1-\phi^2)$ And that the first-order covariance is: ...
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36 views

Why is an ARMA model a parsimonous approximation of an AR model?

I am reading a book on time series and I came across the following: "In addition to being a parsimonous approximation to a high-order AR(p) model, ARMA models...". Why is an ARMA model a (parsimonous) ...
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55 views

When forecasting sequential data is it best to use auto-regressive models or build a more traditional n x p dataset with features?

I'm familiar with the use of auto-regressive models when it comes to forecasting a single vector of time-series data. Is anybody familiar with a more traditional modeling approach, i.e. - creating ...
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27 views

Estimating auto-correlation with unequally spaced data

I'm working on a time series problem where the spacing between observations is usually 12 or 24 hours, but this is not guaranteed. I'd really like to estimate the auto-correlation function, and I've ...
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21 views

How to determine if two time series are significantly related to each other

Based on our knowledge of other characteristics of these two variables, we have reason to believe that changes in admits to a ward has an impact on a certain bad outcome on that ward (these are counts ...
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54 views

find the point at which the curve significantly shoots up

so this is getting a little complex for me and hope someone can help me out. I do not have a mathematical background. I have a time series of daily rainfall for 50 years for a particular location. ...
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60 views

Time Series Forecasting vs Linear Regression Extrapolation

I'm working on some problems involving prediction of future values. I need to get an aggregated total at some point in the future. My question is: what is the best way to predict the future values? ...
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1answer
92 views

relationship between ARMA and AR

I once heard some statements regarding the relationship between ARMA and AR process, such as An average of severl lags of an autoregression forms an ARMA process ...
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196 views

stochastic vs deterministic trend/seasonality in time series forecasting

I have moderate background in time series forecasting. I have looked at several forecasting books, and I don't see the following questions addressed in any of them. I have two questions: How would ...
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22 views

Spatial and temporal effects in water quality data

The data I have is 20 sampling points in a water distribution network that have been sampled weekly during 4 months for different parameters (chlorine, turbidity, disinfection by-products, ...). Some ...
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Predicting one time series from another if they are related - algorithm in R

I am new to time series analysis; I am not even sure if this is even a TS problem. I have looked at other TS posts, but I have a hard time to translate the responses to my needs. For now I am hoping ...
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1answer
32 views

Predicting time series with OpenBUGS

I have a number of fairly short time series (about 4–100 observations) which I need to forecast into the future. I decided to use Bayesian inference, because there is external information about each ...
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35 views

R intercept in arima with xreg

I am trying to understand what the reported intercept is showing when I use arima() with xreg=. The documentation says "If am ...
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1answer
27 views

Repeated measures design with measurements from different groups of animals

In a repeated measured design we measure a particular variable at different time points from the same subjects. In animal experiments, if animals are sacrificed at every time point to measure a ...
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43 views

statistical analysis of events in a given time interval

I am attempting to analyze biological data, to see whether the number of events in a given time interval is more/less than expected based on the overall frequency. How would one approach this? An ...
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Time series pattern identification - SVD/SSA?

I've looked over other posts regarding time series data, and am unsure if the mentioned methods would apply to what I'm trying to do, since I'm not familiar with pattern analysis methods: I have time ...